Atkin-Lehner |
2- 3- 7+ 13- 41- |
Signs for the Atkin-Lehner involutions |
Class |
22386v |
Isogeny class |
Conductor |
22386 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-40036908053495808 = -1 · 216 · 32 · 73 · 136 · 41 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 2 13- 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-562139,162462033] |
[a1,a2,a3,a4,a6] |
Generators |
[382:1681:1] |
Generators of the group modulo torsion |
j |
-19645130164017251655217/40036908053495808 |
j-invariant |
L |
8.4718563330289 |
L(r)(E,1)/r! |
Ω |
0.36361725578227 |
Real period |
R |
0.48539227479289 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
67158m1 |
Quadratic twists by: -3 |